Question: Rewrite the equation by completing the square. $x^{2} -x -20 = 0$ $(x + $
Explanation: $\begin{aligned} x^2 - x -20&=0 \\\\ x^2 - x&=20 \end{aligned}$ Now we want to complete $x^2 - x$ into a perfect square. To do that, we should add $\left(\dfrac{{-1}}{2}\right)^2={\dfrac{1}{4}}$ to it: $x^2{-}x + {\dfrac{1}{4}}=\left(x -\dfrac{1}{2} \right)^2$ $\begin{aligned} x^2 - x&=20 \\\\ x^2 - x + {\dfrac{1}{4}}&=20 + {\dfrac{1}{4}} \\\\ \left(x -\dfrac{1}{2} \right)^2&=\dfrac{81}{4} \end{aligned}$ In conclusion, the equation after completing the square is written as: $\left(x -\dfrac{1}{2} \right)^2=\dfrac{81}{4}$